Solve for $x$ and $y$ using elimination. $\begin{align*}-2x-5y &= 1 \\ 4x+4y &= 8\end{align*}$
Explanation: We can eliminate $x$ when its corresponding coefficients are negative inverses. Recalling our knowledge of least common multiples, multiply the top equation by $2$ and the bottom equation by $1$ $\begin{align*}-4x-10y &= 2\\ 4x+4y &= 8\end{align*}$ Add the top and bottom equations. $-6y = 10$ Divide both sides by $-6$ and reduce as necessary. $y = -\dfrac{5}{3}$ Substitute $-\dfrac{5}{3}$ for $y$ in the top equation. $-2x-5( -\dfrac{5}{3}) = 1$ $-2x+\dfrac{25}{3} = 1$ $-2x = -\dfrac{22}{3}$ $x = \dfrac{11}{3}$ The solution is $\enspace x = \dfrac{11}{3}, \enspace y = -\dfrac{5}{3}$.